## Abstract

Maxwell's equations are transformed from a Cartesian geometry to a Riemannian geometry. A geodetic path in the Riemannian geometry is defined as the raypath on which the electromagnetic energy efficiently travels through the medium. Consistent with the spatial behavior of the Poynting vector, the metric tensor is required to be functionally dependent on the refractive index of the medium. A symmetric nonorthogonal transformation is introduced, in which the metric is a function of an electromagnetic tension. This so-called refractional tension determines the curvature of the geodetic line. To verify the geodetic propagation paths and wavefronts, a spherical object with a refractive index not equal to one is considered. A full 3-D numerical simulation based on a contrast-source integral equation for the electric field vector is used. These experiments corroborate that the geodesics support the actual wavefronts. This result has consequences for the explanation of the light bending around the Sun. Next to Einstein's gravitational tension there is room for an additional refractional tension. In fact, the total potential interaction energy controls the bending of the light. It is shown that this extended model is in excellent agreement with historical electromagnetic deflection measurements.

Original language | English |
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Article number | e2019RS007021 |

Journal | Radio Science |

Volume | 55 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2020 |

## Keywords

- geodetic raypaths
- metric tensor
- ray bending
- refractive object
- Riemannian geometry
- wavefront propagation